Other forms: reciprocating, reciprocated, reciprocates
To reciprocate is to return a feeling or a favour in kind. They did something, and you do the same back.
It is used most often about feelings, and unreciprocated love is one of the standard subjects of every art form there has ever been. It also covers gestures and invitations, so reciprocating hospitality means having them round in return. Engineering has a precise sense, since a reciprocating engine has pistons moving back and forth. The noun is reciprocity, which in trade means each side granting the other the same terms.
1verbreciprocateTo respond to an action or feeling with a matching one.
“She smiled and he reciprocated.”
Reciprocate has the back-and-forth built into it. Latin reciprocus may come from the phrase reque proque, back and forth, so reciprocating is quite literally going both ways.
Latin
recīprocātus
English, today
reciprocate
Built from
From Latin recīprocātus, perfect passive participle of recīprocō (“to move back and forth”) (see -ate), from reciprocus + -ō, itself possibly from a phrase such as reque proque (“back and forth”), from re- (“back”), prō (“forwards”) and -que (“and”). See also reciprocal. Compare French réciproquer.
Etymology from Wiktionary, CC BY-SA